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Simplifying (7k + -3)(k + 4) = 0 Reorder the terms: (-3 + 7k)(k + 4) = 0 Reorder the terms: (-3 + 7k)(4 + k) = 0 Multiply (-3 + 7k) * (4 + k) (-3(4 + k) + 7k * (4 + k)) = 0 ((4 * -3 + k * -3) + 7k * (4 + k)) = 0 ((-12 + -3k) + 7k * (4 + k)) = 0 (-12 + -3k + (4 * 7k + k * 7k)) = 0 (-12 + -3k + (28k + 7k2)) = 0 Combine like terms: -3k + 28k = 25k (-12 + 25k + 7k2) = 0 Solving -12 + 25k + 7k2 = 0 Solving for variable 'k'. Factor a trinomial. (-4 + -1k)(3 + -7k) = 0Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve: Simplifying -4 + -1k = 0 Solving -4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1k = 0 + 4 -1k = 0 + 4 Combine like terms: 0 + 4 = 4 -1k = 4 Divide each side by '-1'. k = -4 Simplifying k = -4Subproblem 2
Set the factor '(3 + -7k)' equal to zero and attempt to solve: Simplifying 3 + -7k = 0 Solving 3 + -7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7k = 0 + -3 -7k = 0 + -3 Combine like terms: 0 + -3 = -3 -7k = -3 Divide each side by '-7'. k = 0.4285714286 Simplifying k = 0.4285714286Solution
k = {-4, 0.4285714286}
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